Answer
$\sqrt{2}$
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a perfect square:
$-\sqrt{18}+2\sqrt8\\
=-\sqrt{9\cdot 2}+2\sqrt{4\cdot 2}\\
=-\sqrt{3^2\cdot 2}+2\sqrt{2^2\cdot 2}\\$
Use the rule $\sqrt{a\cdot b}=\sqrt{a} \cdot \sqrt{b}$ then simplify:
$=-\sqrt{3^2}\cdot \sqrt{2}+2\sqrt{2^2}\cdot \sqrt{2}$
$=-3\cdot \sqrt{2}+2\cdot2\cdot \sqrt{2}$
$=-3\sqrt{2}+4\sqrt{2}$
Factor out $\sqrt{2}$ then simplify.
$=\sqrt{2}(-3+4)$
$=\sqrt{2}(1)$
$=\sqrt{2}$
Hence, the correct answer is $\sqrt{2}$.
